The benefit of using the 970's DVI switching with your HDMI-equipped DVD player is that you can still connect a second DVI or HDMI-equipped component (HD cable box, HD satellite receiver, or later this year a Blu-ray or HD-DVD player) even though your TV doesn't have another input. If you don't plan to add anything else, you can of course go straight to the TV with the HDMI signal.
The Denon
DVD-1920 supports both SACD and DVD-Audio, both of which are under some heavy restrictions as to how the signal can be output. The only ways to get the full resolution audio signal out of the player are to use multichannel analog outputs or an approved digital output (IEEE-1394, HDMI 1.1 for DVD-Audio, HDMI 1.2 for DVD-Audio and SACD, or a proprietary format like Denon Link), none of which either the 1920 or 970 support. In the case of the DVD-1920 (and most other universal players), the multichannel analog output also includes decoders for Dolby Digital and DTS, although I don't recommend using them with the 970 mainly because the digital output allow you to use processing modes like Pro Logic IIx. If you are not using the multichannel analog output with DVD-Audio or SACD, however, you are not truly getting the high resolution audio available with these formats - SACD typically provides no signal at all to the digital output, and DVD-Audio only provides a Dolby Digital 2.0 track.